SOLUTION OF PENDULUM EQUATION USING THE RITZ-GALERKIN METHOD

Abstract

Most of engineering problems, especially some oscillation equations are nonlinear, and in most cases, it is difficult to solve such equations, especially analytically. This paper considers the response of a nonlinear to random excitation. One of the well-known methods to solve nonlinear problems is perturbation method Ritz-Galerkin type methods, both continuous and discrete in time, are considered for approximating solutions of linear and nonlinear problems. Bounds reducing the estimation of the error to questions in approximation theory are derived for the several methods studied. These methods include procedures that lead to linear algebraic equations even for nonlinear problems. A number of computational questions related to these procedures are also discussed.